Universal Gates for Ising Tqft via Time-Tilted Interferometry

1. A logical gate for a quantum computer, the logical gate comprising: an input current source for injecting an input current into a first edge of a fractional quantum Hall effect (FQHE) fluid; an output current source for removing an output current drained from a second edge of the FQHE fluid; a first antidot defined by a first absence of FQHE fluid; a second antidot defined by a second absence of FQHE fluid; a voltage supply for adjusting an electrical potential confining the FQHE fluid to form a Polyakov loop between the antidots; means for determining from the output current a quantum state of the Polyakov loop.

2. The logical gate of claim 1 , wherein the voltage supply enables adjustment of the electrical potential to cause a separation between the antidots.

3. The logical gate of claim 2 , wherein the separation prevents tunneling between the antidots.

4. The logical gate of claim 2 , wherein the separation is a gap in the FQHE fluid between the antidots.

5. The logical gate of claim 4 , wherein the voltage supply enables adjustment of the electrical potential to heal the gap.

6. The logical gate of claim 1 , wherein measurement of the output current causes the particle to converge to an eigenstate.

7. The logical gate of claim 1 , wherein the FQHE fluid is formed at an interface between first and second crystals.

8. The logical gate of claim 7 , wherein the first crystal is a gallium arsenide crystal.

9. The logical gate of claim 8 , wherein the second crystal is an aluminum gallium arsenide crystal.

10. The logical gate of claim 1 , further comprising: means for determining whether the quantum state of the Polyakov loop corresponds to a state carrying trivial SU(2) charge |1>.

11. The logical gate of claim 1 , further comprising: means for determining whether the quantum state of the Polyakov loop corresponds to a state carrying a fermionic SU(2) charge |ε>.

12. The logical gate of claim 1 , wherein the FQHE fluid is a ν=5/2 quantum Hall effect fluid.

13. A method for read out of a logical gate in a quantum computer, the method comprising: forming a Polyakov loop in the space-time of a fractional quantum Hall effect (FQHE) fluid; determining a quantum state of the Polyakov loop.

14. The method of claim 13 , wherein forming the Polyakov loop comprises adjusting an electrical potential confining the FQHE fluid to form the Polyakov loop.

15. The method of claim 13 , wherein forming the Polyakov loop comprises: forming a first antidot in the FQHE fluid; forming a second antidot in the FQHE fluid; separating the antidots to form a gap in the FQHE fluid between the antidots; and after separating the antidots to form the gap, bringing the antidots together to heal the gap.

16. The method of claim 15 , wherein determining the quantum state of the Polyakov loop comprises: injecting an input current into a first edge of the FQHE fluid near the first antidot; and removing an output current from a second edge of the FQHE fluid near the second antidot; and deducing the quantum state of the Polyakov loop from the output current.

17. A method for implementing a logical gate in a quantum computer, the method comprising: providing a logical gate for a quantum computer, said logical gate comprising a fractional quantum Hall effect (FQHE) fluid having first and second antidots disposed therein; forming a Polyakov loop between the antidots; and affecting a quantum state of the Polyakov loop by causing a quasi-particle to tunnel between the first and second antidots.

18. The method of claim 17 , wherein forming the Polyakov loop comprises: establishing a first condition wherein tunneling can occur between the antidots; then establishing a second condition wherein tunneling cannot occur between antidots; then establishing a third condition wherein tunneling can re-occur between anti-dots.

19. The method of claim 18 , further comprising: measuring an output current from an edge of the FQHE fluid near the second anti-dot after the third condition has been established.

20. The method of claim 18 , further comprising: injecting an input current into an edge of the FQHE fluid near the first anti-dot before the second condition is established.